Methods for sorting nanotubes by electronic type

ABSTRACT

A method of separating carbon nanotubes by electronic type includes centrifuging a carbon nanotube composition in contact with a first fluid medium comprising a first density gradient; and separating the carbon nanotube composition into two or more separation fractions. The carbon nanotube composition comprises two or more non-ionic amphiphilic surface active components and a carbon nanotube population comprising double-walled carbon nanotubes having a semiconducting outer wall (s-DWCNTs), and double-walled carbon nanotubes having a metallic outer wall (m-DWCNTs). The two or more separation fractions comprise a first separation fraction comprising a carbon nanotube subpopulation comprising a higher percentage of s-DWCNTs than the carbon nanotube population, and a second separation fraction comprising a carbon nanotube subpopulation comprising a higher percentage of m-DWCNTs than the carbon nanotube population.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a divisional of and claims priority to and thebenefit of patent application Ser. No. 14/625,333, filed Feb. 18, 2015,now allowed, which is a divisional of and claims priority to and thebenefit of patent application Ser. No. 12/536,250, filed Aug. 5, 2009,now abandoned, which claims priority to and the benefit of provisionalpatent application Ser. No. 61/086,302, filed Aug. 5, 2008, each ofwhich is incorporated herein in its entirety by reference.

STATEMENT AS TO RIGHTS UNDER FEDERALLY-SPONSORED RESEARCH

This invention was made with government support under EEC-0647560 andDMR-0706067 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

FIELD OF THE INVENTION

The present invention relates generally to the field of nanotechnology,and more particularly to methods for sorting nanotubes by electronictype and applications of the same.

BACKGROUND OF THE INVENTION

Carbon nanotubes are one-dimensional nanomaterials consisting ofcylinders of graphene. Depending on their diameter and helicity, carbonnanotubes consisting of a single graphene tubule, known as single-walledcarbon nanotubes (SWCNTs), can behave either as metals or semiconductorswhose band gap varies inversely with tube diameter. Multi-walled carbonnanotubes, which consist of multiple concentric graphene cylinders,typically possess much larger diameters than SWCNTs.

Accordingly, these carbon nanotubes demonstrate metallic or small bandgap semiconducting behavior, and are mechanically stronger than SWCNTs.Developments in carbon nanotube synthesis have enabled the preferentialproduction of multi-walled carbon nanotubes consisting of two walls.These double-walled carbon nanotubes (DWCNTs) can be synthesized usingmethods including chemical vapor deposition, electric arc discharge, andcoalescence of chains of C60 inside SWCNTs. DWCNTs have garneredincreasing attention for applications because their structure providesthem with characteristics situated between those of SWCNTs andmulti-walled carbon nanotubes having three or more walls (MWCNTs).Compared to SWCNTs and MWCNTs, DWCNTs have demonstrated betterperformance parameters in field-effect transistors, improved spatialresolution and longer scanning lifetimes as atomic force microscope(AFM) tips, and more desirable field emission characteristics.

Despite their promising applications, current methods of synthesizingDWCNTs also produce significant quantities of unwanted SWCNTs andMWCNTs. Multiple groups have succeeded in increasing the proportion ofDWCNTs following synthesis using high temperature oxidation, whichpreferentially destroys the more thermally unstable SWCNT impurities.However, these oxidative treatments can degrade the electrical andoptical properties of DWCNTs, and are ineffective at removing MWCNTsbecause DWCNTs and MWCNTs exhibit similar thermal stabilities.

As a result, more refined separation methods are required to providenanotube populations that are highly enriched with DWCNTs. Furthermore,beyond separation by wall number, practical applications also requireDWCNT materials that are enriched according to chirality, diameterand/or electronic type to ensure that their electrical and opticalproperties are uniform.

SUMMARY OF THE INVENTION

In light of the foregoing, the present teachings relate to methods ofseparating nanotubes by wall number. In particular, the present methodscan provide nanotube subpopulations that are selectively enriched withdouble-walled nanotubes (DWNTs), multi-walled nanotubes having three ormore walls (MWNTs), or single-walled nanotubes (SWNTs) from a mixed (orpolydisperse) nanotube population including DWNTs, MWNTs, and SWNTs.Because MWNTs generally have larger mean outer wall diameters thanDWNTs, and DWNTs generally have larger mean outer wall diameters thanSWNTs, in part, the present methods can be directed to separatingnanotubes by diameter. For nanotubes of different wall numbers that mayhave overlapping outer wall diameter ranges, the present methods areable to separate among them by wall number. In some embodiments, thepresent methods also can provide DWNT subpopulations that areselectively enriched by one or more characteristics such as a certainouter wall diameter range, a selected outer wall electronic type, and/ora selected outer wall chirality (n,m) type.

Accordingly, in some embodiments, the present methods allow separationof double-walled carbon nanotubes (DWCNTs) from a mixed population ofcarbon nanotubes having different wall numbers, thereby providing atleast one subpopulation of carbon nanotubes enriched with DWCNTs, thatis, the enriched subpopulation has a higher percentage of DWCNTscompared to the mixed population. Because of the non-destructive natureof the present methods, carbon nanotubes other than DWCNTs, e.g., SWCNTsand/or MWCNTs, also can be separated and recovered from the mixedpopulation, thereby providing at least one subpopulation of carbonnanotubes that is enriched with SWCNTs or MWCNTs. Concurrently (i.e., ina single separation cycle) or in different separation cycles, thepresent methods further allow separating the DWCNTs by one or morecharacteristics such as diameter, band gap, chirality and/or electronictype, thereby providing DWCNT subpopulations that are enriched byselected characteristic(s). The high-purity DWCNT populations accordingto the present teachings can offer various improved properties overprior art DWCNT populations. These improved properties can be realizedwhen incorporated into devices and applications such as light emittingdiodes, photovoltaics, electrostatic discharge coatings, atomic forcemicroscope tips, flat panel displays, touch screens, electromagneticscreening applications, field-emission displays, biosensors,field-effect transistors, transparent conductors or functional glass,and other functional composite materials including drug deliverymaterials.

The present methods can be applied to a mixed population of carbonnanotubes that include DWCNTs and one or more types of carbon nanotubeshaving a wall number other than two. In some embodiments, the mixedpopulation can include DWCNTs and SWCNTs. In other embodiments, themixed population can include DWCNTs and MWCNTs. In yet otherembodiments, the mixed population can include DWCNTs and both SWCNTs andMWCNTs. The mixed population generally includes a certain percentage ofDWCNTs but also a significant quantity of SWCNTs and/or MWCNTs. However,in certain embodiments, the mixed population of carbon nanotubes caninclude a high percentage of DWCNTs, where the DWCNT population exhibitspolydispersity in electronic type, diameter, and/or chirality. In suchembodiments, the present methods can be applied to separate thepolydisperse DWCNT population by one or more of electronic type,diameter, and chirality.

A mixed or polydisperse population of carbon nanotubes can be firstcontacted with one or more surface active components in a solvent toform a dispersion. The one or more surface active components can beselected for their ability to associate differentially with carbonnanotubes of different wall numbers such that individual carbonnanotubes of different wall numbers, upon association with the surfaceactive components, can exhibit different buoyant densities in thesolvent.

In certain embodiments, the one or more surface active components can besubstantially insensitive to carbon nanotubes of different electronictypes such that semiconducting carbon nanotubes and metallic carbonnanotubes of the same wall number can have substantially similar buoyantdensities in the solvent when associated with the one or more surfaceactive components. In embodiments where the mixed population includesSWCNTs and DWCNTs having overlapping outer wall diameter ranges, the oneor more surface active components can confer sufficiently differentbuoyant densities to the encapsulated SWCNTs and DWCNTs to allowseparation.

Subsequently, the carbon nanotube dispersion is subjected to densitygradient ultracentrifugation (DGU) by introducing the dispersion into afluid medium including a density gradient. The density gradient caninclude a linear gradient including three or more layers of differentdensities. The layers can be prepared with different concentrations of adensity gradient medium such as iodixanol. In certain embodiments, thedispersion can be introduced into the density gradient at a density thatis different from the respective buoyant densities of the various typesof carbon nanotubes in the mixed population as they are associated withthe one or more surface active components. For example, the dispersioncan be introduced into the fluid medium at a density that is lower thanthe respective buoyant densities of the various types of carbonnanotubes in the mixed population as associated with the one or moresurface active components. In certain embodiments, the dispersion can belayered on top of the linear density gradient.

Once introduced, the fluid medium can be agitated, for example, byultracentrifugation, to allow separation of the carbon nanotubes by wallnumber along the density gradient. After sufficient agitation, nanotubesof different wall numbers are allowed to settle into a plurality ofseparation fractions, where at least one of the separation fractions isenriched with nanotubes of a specific wall number. The separationfractions can be visibly distinguishable among each other by human eye.For example, two or more separation fractions can be distinguishable bydifferent colors and/or different shades of a particular color in thevisible spectrum.

A single separation cycle according to the present methods often leadsto enrichment that is satisfactory for most applications. Accordingly,following one separation cycle, one or more separation fractions thathave been enriched with DWCNTs can be collected from the densitygradient. For example, where the mixed population includes 100 carbonnanotubes of any kind, 50 or 50% of the carbon nanotubes can be DWCNTs.In accordance with the present teachings, after a single separationcycle, the mixed population can separate into multiple separablesubpopulations, wherein at least one of them is enriched with DWCNTs.For example, in a subpopulation enriched with DWCNTs, there can be 50carbon nanotubes, among which 40 (or 80%) can be DWCNTs. The proportionof DWCNTs, therefore, has increased from 50% to 80% via one separationcycle, or an enrichment factor of 0.6. In practice, the enrichmentfactor can be calculated from spectroscopic measurements such as opticalabsorbance, fluorescence, and Raman spectroscopy.

Accordingly, a DWCNT-enriched fraction can be enriched with at least 50%more (an enrichment factor of 0.5), at least 75% more (an enrichmentfactor of 0.75), at least 100% more (an enrichment factor of 1.0), or atleast 200% more (an enrichment factor of 2.0) DWCNTs compared to thepercent composition of DWCNTs in the initial mixed population. Incertain embodiments, the DWCNT-enriched separation fraction can includegreater than about 60%, greater than about 70%, greater than about 80%,greater than about 85%, greater than about 87%, greater than about 90%,greater than about 92%, greater than about 95%, greater than about 97%,or greater than about 99% encapsulated DWCNTs. In some embodiments, theDWCNT-enriched separation fraction can be substantially free ofencapsulated SWCNTs. For example, the separation fraction can includeless than about 10%, less than about 5%, less than about 3%, less thanabout 2%, or less than about 1% encapsulated SWCNTs. In particularembodiments, the DWCNT-enriched separation fraction can be substantiallyfree of SWCNTs having diameter ranges overlapping with the outer walldiameter ranges of the DWCNTs in the enriched separation fraction.

Performing one or more additional sorting or separation cycles canimprove the quality of the separation and provide increasingly enrichedseparation fractions. Because bundles of carbon nanotubes tend to formover time, the DWCNT-enriched separation fraction can include impuritiessuch as bundled SWCNTs. To remove these impurities, the DWCNT-enrichedseparation fraction can be introduced into a second fluid mediumincluding a second density gradient and centrifuged. In particularembodiments, the DWCNT-enriched separation fraction can be introduced ata density that is higher than the buoyant density of DWCNTs in thesecond fluid medium. In certain embodiments, the DWCNT-enrichedseparation fraction can be introduced into the fluid medium at thebottom of the density gradient. After sufficient agitation, the DWCNTsand bundled SWCNTs can settle into a plurality of separation fractionsthat are visibly distinguishable by human eye, allowing collection of ahighly DWCNT-enriched separation fraction that is substantially free ofbundled SWCNTs. For example, at least about 80% of all the nanotubematerials in the highly enriched-DWCNTs separation fraction can includeDWCNTs.

In addition to broad distributions of chiralities and diameters, currentsynthetic methods typically produce a 1:2 ratio ofmetallic-to-semiconducting carbon nanotubes. The present teachingsprovide methods of separating carbon nanotubes by wall number and byelectronic type, and methods of separating double-walled carbonnanotubes by electronic type. As used herein, when a DWCNT is specifiedto be of a particular electronic type, the electronic type should beunderstood as that of the outer wall or shell only unless statedotherwise.

For example, a mixed population of carbon nanotubes that includessemiconducting SWCNTs (s-SWCNTs), metallic SWCNTs (m-SWCNTs),semiconducting DWCNTs (s-DWCNTs) and metallic DWCNTs (m-DWCNTs), or apopulation of DWCNTs including s-DWCNTs and m-DWCNTs, can be contactedwith two or more surface active components in a solvent to form adispersion. As described above with respect to methods of separatingcarbon nanotubes by wall number and by diameter, the two or more surfaceactive components typically associate with the carbon nanotubesnon-covalently, providing debundled individual carbon nanotubesencapsulated by the two or more surface active components.

The two or more surface active components can be selected for theirability to associate differentially with carbon nanotubes by electronictype as well as simultaneously by wall number and by electronic typesuch that encapsulated individual carbon nanotubes of differentelectronic types (and different wall numbers) exhibit different buoyantdensities in the solvent. In certain embodiments, the two or moresurface active components can include a planar surface active component(e.g., a salt of cholic acid) and a linear surface active component(e.g., a surfactant having an anionic or cationic head group and alinear (flexible or rigid) aliphatic tail group). In some embodiments,the relative ratio of the two or more surface active components can beselected to cause metallic carbon nanotubes to have a different (higheror lower) buoyant density than semiconducting carbon nanotubesregardless of wall number. In certain embodiments, the relative ratio ofthe two or more surface active components can be selected to causemetallic carbon nanotubes to have a different (higher or lower) buoyantdensity than semiconducting carbon nanotubes of the same wall number.

The dispersion including the encapsulated carbon nanotubes then can besubjected to density gradient ultracentrifugation (DGU) processingsimilar to what is described above. After sufficient agitation, carbonnanotubes of different electronic types (and different wall numbers) cansettle into a plurality of separation fractions that are visiblydistinguishable by human eye, allowing collection of separationfractions that include primarily DWCNTs having an outer wall of aparticular electronic type. For example, in some embodiments, thepresent teachings can provide a population of DWCNTs where greater thanabout 70%, greater than about 80%, greater than about 85%, greater thanabout 93%, or greater than about 97% of the DWCNTs have a semiconductingouter wall. In some embodiments, the present teachings can provide apopulation of DWCNTs where greater than about 50%, greater than about75%, greater than about 90%, greater than about 97%, or greater thanabout 99% of the DWCNTs have a metallic outer wall. In some embodiments,the separation fraction can consist essentially of DWCNTs having anouter wall of a particular electronic type. In various embodiments, theDWCNT populations described herein can have a mean outer wall diameterof less than about 1.7 nm.

Using the appropriate surface active component(s), the present teachingsalso can provide populations of DWCNTs where greater than about 30%,greater than about 50%, greater than about 75%, or greater than about90% of the DWCNTs have outer walls having the same chirality (n,m) type.

The various methods described herein can be used to sort bulk quantitiesof nanotubes, for example, populations of nanotubes that include morethan about 10¹² nanotubes, more than about 10¹³ nanotubes, more thanabout 10¹⁴ nanotubes, more than about 10¹⁵ nanotubes, more than about10¹⁶ nanotubes or more than about 10¹⁷ nanotubes; or equivalently, morethan about 10 μg, more than about 100 μg, more than about 1 mg, morethan about 10 mg, more than about 100 mg, or more than about 1 gram ofnanotubes by mass, in a single separation cycle.

The DWCNT populations of the present teachings can be dispersed in asolvent, for example, by contacting them with one or more surface activecomponents including those described herein, to provide coloredtranslucent solutions. The present DWCNT populations can be incorporatedinto various articles of manufacture including various electronic,optical, or optoelectronic devices such as field-effect transistors,transparent conductors, interconnect devices, sensors, light-emittingdiodes, and solar cells, to improve one or more electronic and/oroptical properties of these devices.

In one aspect of the invention, a method of separating carbon nanotubesby electronic type includes centrifuging a carbon nanotube compositionin contact with a first fluid medium comprising a first densitygradient; and separating the carbon nanotube composition into two ormore separation fractions. The carbon nanotube composition comprises twoor more non-ionic amphiphilic surface active components and a carbonnanotube population comprising double-walled carbon nanotubes having asemiconducting outer wall (s-DWCNTs), and double-walled carbon nanotubeshaving a metallic outer wall (m-DWCNTs). The two or more separationfractions comprise a first separation fraction comprising a carbonnanotube subpopulation comprising a higher percentage of s-DWCNTs thanthe carbon nanotube population, and a second separation fractioncomprising a carbon nanotube subpopulation comprising a higherpercentage of m-DWCNTs than the carbon nanotube population.

In one embodiment, the two or more surface active components comprise aplanar surface active component and a linear surface active component.

In one embodiment, the carbon nanotube population comprisessemiconducting single-walled carbon nanotubes (s-SWCNTs) and metallicsingle-walled carbon nanotubes (m-SWCNTs), and wherein after thecentrifuging step, the carbon nanotube composition is separated by wallnumber and by outer wall electronic type into at least four separationfractions, the at least four separation fractions comprising the firstseparation fraction, the second separation fraction, a third separationfraction comprising a carbon nanotube subpopulation comprising a higherpercentage of s-SWCNTs than the carbon nanotube population, and a fourthseparation fraction comprising a carbon nanotube subpopulationcomprising a higher percentage of m-SWCNTs than the carbon nanotubepopulation.

In one embodiment, the relative ratio of the two or more surface activecomponents is selected to cause metallic carbon nanotubes to have alower buoyant density than semiconducting carbon nanotubes regardless ofwall number.

In one embodiment, the relative ratio of the two or more surface activecomponents is selected to cause semiconducting carbon nanotubes to havea lower buoyant density than metallic carbon nanotubes of the same wallnumber.

In one embodiment, the relative ratio of the two or more surface activecomponents is selected to cause metallic carbon nanotubes to have alower buoyant density than semiconducting carbon nanotubes of the samewall number.

In one embodiment, the relative ratio of the two or more surface activecomponents is selected to cause semiconducting carbon nanotubes to havea lower buoyant density than metallic carbon nanotubes regardless ofwall number.

Other objects, features, and advantages of the present teachings will bemore fully understood from the following figures, description, examples,and claims.

BRIEF DESCRIPTION OF DRAWINGS

It should be understood that certain drawings are not necessarily toscale, with emphasis generally being placed upon illustrating theprinciples of the present teachings. The drawings are not intended tolimit the scope of the present teachings in any way.

FIGS. 1A-1C are schematic cross-sectional diagrams showing howsurface-active components can associate differentially with asmall-diameter single-walled nanotube (FIG. 1A), a large-diametersingle-walled nanotube (FIG. 1B), and a double-walled nanotube (FIG.1C).

FIGS. 2A-2B illustrate an embodiment of the present methods by whichcarbon nanotubes can be sorted by wall number. FIG. 2A is a photographshowing separation of double-walled carbon nanotubes and single-walledcarbon nanotubes (visible to human eye as distinct bands of materials)from a polydisperse sample after one separation cycle according to thepresent methods. FIG. 2B compares the optical absorbance spectra ofsorted nanotube materials (collected from the centrifuge tube shown inFIG. 2A from the bands indicated) with the unsorted starting nanotubematerial.

FIGS. 3A-3D show Raman spectra of single-walled carbon nanotubesproduced by high-pressure carbon monoxide catalysis (HiPco-SWCNTs),single-walled carbon nanotubes produced by arc discharge (AD-SWCNTs),and two subpopulations from a mixed nanotube population includingdouble-walled carbon nanotubes and single-walled carbon nanotubes. Usingmethods according to the present teachings, one of the subpopulations isenriched with DWCNTs (DGU-DWCNTs), whereas the other subpopulation isenriched with SWCNTs (DGU-SWCNTs). FIG. 3A and FIG. 3C display theradial breathing mode (RBM) regions for all four nanotube materials atexcitation wavelengths of 514.5 nm and 750 nm, respectively. FIG. 3B andFIG. 3D show spectra from the carbon nanotube tangential modes beforeand after acid treatment.

FIGS. 4A-4D show optical absorbance spectra of thin films ofHiPco-SWCNTs, AD-SWCNTs, DGU-SWCNTs, and DGU-DWCNTs before (solidcurves) and after (dashed curves) exposure to thionyl chloride.

FIG. 5 shows a histogram summarizing the results of a statisticalanalysis of the length distribution of single-walled carbon nanotubes(open bars) and double-walled carbon nanotubes (shaded bars) aftersorting according to the present teachings.

FIGS. 6A-6B show sheet resistance versus transmittance graphs fortransparent conductive films prepared from DGU-SWCNTs (triangles),DGU-DWCNTs (squares), and the starting unsorted DWCNT population(circles) at a wavelength of 550 nm. FIG. 6A shows the transparentconductor performance data for pristine (updoped) populations. FIG. 6Bshows the transparent conductor performance data following doping withthionyl chloride.

FIGS. 7A-7D illustrate certain embodiments of the present teachings bywhich carbon nanotubes can be sorted by both wall number and outer wallelectronic type. FIG. 7A and FIG. 7C are photographs showing separationof double-walled carbon nanotubes having a semiconducting outer wall,double-walled carbon nanotubes having a metallic outer wall,semiconducting single-walled carbon nanotubes, and metallicsingle-walled carbon nanotubes (visible to human eye as distinct bandsof materials) from a polydisperse sample after one separation cycleaccording to the present methods. In FIG. 7A, the sorting conditions areadapted to favor separation of DWCNTs having a semiconducting outerwall. In FIG. 7B, the sorting conditions are adapted to favor separationof DWCNTs having a metallic outer wall. FIG. 7B and FIG. 7D show theoptical absorbance data of sorted materials collected from thecentrifuge tubes shown in FIG. 7A and FIG. 7C, respectively, from thebands indicated.

FIGS. 8A-8B show Raman spectra of DGU-DWCNTs (FIG. 8B) as compared tostate-of-the-art high-purity as-synthesized DWCNTs (FIG. 8A).

FIG. 9 shows the optical absorbance of sorted DWCNT samples in aqueoussolution that are highly enriched by the outer wall electronic type,specifically, a sample highly enriched with DWCNTs having asemiconducting outer wall (s-DWCNT, solid curve), and a sample highlyenriched with DWCNTs having a metallic outer wall (m-DWCNT, dashedcurve).

FIG. 10A shows the optical absorbance of a DWCNT sample in thin filmform that is highly enriched with s-DWCNT before (solid curve) and after(dashed curve) doping treatment with thionyl chloride. FIG. 10B showsthe optical absorbance of a DWCNT sample in thin film form that ishighly enriched with m-DWCNT before (solid curve) and after (dashedcurve) doping treatment with thionyl chloride.

FIG. 11 shows Raman spectra in the RBM region obtained from s-DWCNTs(solid curve) and m-DWCNTs (dashed curve) at an excitation wavelength of514.5 nm.

FIGS. 12A-12B show data from field-effect transistors made from s-DWCNTand m-DWCNT thin films. FIG. 12A shows the source-drain current (IDs) asa function of the gate bias (VG) at different source-drain voltages(Vps) for field-effect transistors having a 4 μm×250 pm channel andincluding a thin film of s-DWCNT (s-DWCNT FET, solid curves) or a thinfilm of m-DWCNT (m-DWCNT FET, dashed curves) as the active layer. FIG.12B shows the maximum current as a function of on/off ratio for thes-DWCNT FET (open symbols) and the m-DWCNT FET (closed symbols). Squaresare from devices with a channel length of 2 μm and triangles are fromdevices with a channel length of 4 pm. All devices had a channel widthof 250 pm.

DETAILED DESCRIPTION OF THE INVENTION

Throughout the description, where compositions are described as having,including, or comprising specific components, or where processes aredescribed as having, including, or comprising specific process steps, itis contemplated that compositions of the present teachings also consistessentially of, or consist of, the recited components, and that theprocesses of the present teachings also consist essentially of, orconsist of, the recited processing steps.

In the application, where an element or component is said to be includedin and/or selected from a list of recited elements or components, itshould be understood that the element or component can be any one of therecited elements or components or can be selected from a groupconsisting of two or more of the recited elements or components.Further, it should be understood that elements and/or features of acomposition, an apparatus, or a method described herein can be combinedin a variety of ways without departing from the spirit and scope of thepresent teachings, whether explicit or implicit herein.

The use of the terms “include,” “includes,” “including,” “have,” “has,”“having,” “contain,” “contains,” or “containing” should be generallyunderstood as open-ended and non-limiting unless specifically statedotherwise.

The use of the singular herein includes the plural (and vice versa)unless specifically stated otherwise. In addition, where the use of theterm “about” is before a quantitative value, the present teachings alsoinclude the specific quantitative value itself, unless specificallystated otherwise.

It should be understood that the order of steps or order for performingcertain actions is immaterial so long as the present teachings remainoperable. Moreover, two or more steps or actions may be conductedsimultaneously.

As used herein, a “nanotube” refers to an elongated hollow structure,for example, a cylindrical tube, having a nanoscale diameter, e.g., lessthan about 50 nm and usually less than about 10 nm, and typically a highaspect ratio. The present teachings can be useful for separating variouselemental or molecular nanotubes including, but not limited to, carbon,boron, BN, WS₂, and MoS₂. As such, while the description and examplesherein may refer specifically to carbon nanotubes, the present teachingsare intended to encompass separation of nanotubes in general regardlessof their composition.

As used herein, a “population” of nanotubes can include about greaterthan about 10⁸ nanotubes, greater than about 10⁹ nanotubes, greater thanabout 10¹⁰ nanotubes, greater than about 10¹¹ nanotubes, greater thanabout 10¹² nanotubes, greater than about 10¹³ nanotubes, greater thanabout 10¹⁴ nanotubes, greater than about 10¹⁵ nanotubes, greater thanabout 10¹⁶ nanotubes, or greater than about 10¹⁷ nanotubes. Further, byweight, a population of nanotubes can have a mass of about 0.001 μg,greater than about 0.01 μg, greater than about 0.1 μg, greater thanabout 1 μg, greater than about 10 μg, greater than about 100 μg ,greater than about 1 mg, greater than about 10 mg, greater than about100 mg, or greater than about 1 g. In certain embodiments of the presentteachings, a separation cycle can be used to sort bulk quantites ofnanotubes, for populations of nanotubes that include more than about10¹² nanotubes, more than about 10¹³ nanotubes, more than about 10¹⁴nanotubes, more than about 10¹⁵ nanotubes, more than about 10¹⁶nanotubes or more than about 10¹⁷ nanotubes; or equivalently, more thanabout 10 lug, more than about 100 lug, more than about 1 mg, more thanabout 10 mg, more than about 100 mg, or more than about 1 gram ofnanotubes by mass.

As used herein, “enrichment” or “enriched” refers to an increase in thestatistical proportion of nanotubes comprising one or more specificcharacteristics in a fraction obtained from a sample as compared to thesample as a whole. As described herein, a nanotube subpopulation that is“enriched” according to the present teachings by one or more properties,such as wall number, diameter, electronic type, chirality, orcombinations thereof, means that the subpopulation (i.e., the enrichedpopulation) has a higher percentage of nanotubes having the one or moreproperties when compared to the starting population (i.e., the mixedpopulation) from which the subpopulation is derived.

Various methods have been used to different degrees of success forseparating SWCNTs by one or more characteristics such as chirality,diameter, and electronic type. However, the extension of separationmethods for SWCNTs to DWCNTs and MWCNTs can be described asunpredictable at best. Because of their more complicated structures andintershell interactions, DWCNTs and MWCNTs can be expected to responddifferently to a particular separation method when compared to SWCNTs.Using DWCNTs as an example, four distinct outer shell-inner shellcombinations are possible, namely, metallic (M)-semiconducting (S), M-M,S-M, and S-S. It is not well known how the electronic type of the innershell affects the electronic properties of a DWCNT as a whole. See e.g.,Wang et al., J. Phys. Chem. B, vol. 109(37): 17361-17365 (2005).Similarly, it is not well known how the inner wall diameter and theinterwall spacing modify the properties of a DWCNT. See e.g., Okada etal., Phys. Rev. Lett., vol. 91(21): 216801(1)-216801(4) (2003). Forexample, it is often unpredictable how a SWCNT and an otherwise similarDWCNT, e.g., the outer shell of the DWCNT has similar characteristics asthe SWCNT but for the presence of the inner shell, react differently toa particular functionalizing group. See e.g., Pfeiffer et al., Phys.Rev. B, vol. 72, 161404(R)(1)-161404(R)(4) (2005). To the inventors'knowledge, there has been no reported method for separating carbonnanotubes by wall number that allows isolation of DWCNTs and/or MWCNTs,or for separating DWCNTs and/or MWCNTs by one or more desirablecharacteristics of the outer shell such as chirality, diameter, and/orelectronic type. In addition, it is unclear whether any of theseparation methods that have been used with SWCNTs can distinguishbetween SWCNTS and DWCNTs and/or MWCNTs having similar outer shellcharacteristics.

The present teachings provide methods related to sorting nanotubes, inparticular, carbon nanotubes, according to their wall number. Morespecifically, it has been found that density gradientultracentrifugation (DGU) can be used to separate carbon nanotubesaccording to their wall number, thereby providing, for example, aseparation fraction that includes primarily DWCNTs from an initial mixedpopulation that includes DWCNTs, SWCNTs and/or MWCNTs. Furthermore, ithas been found that with the appropriate choice of surface activecomponent(s), the present teachings can lead to simultaneous separation(i.e., in a single separation cycle) of carbon nanotubes by wall numberand at least one other property, e.g., diameter or electronic type.Accordingly, certain embodiments of the present methods can enablesorting of carbon nanotubes by both wall number and (outer wall)electronic type, while certain embodiments of the present methods canenable sorting of carbon nanotubes by both wall number and (outer wall)diameter. In addition, various embodiments of the present methods canseparate carbon nanotubes of a specified wall number, for example,DWCNTs, based on one or more other properties such as electronic type,diameter and/or chirality.

In particular, as-synthesized DWCNT samples typically include unwantedSWCNTs having diameter ranges that overlap with the outer wall diameterranges of at least a portion of the DWCNTs. Certain embodiments of thepresent teachings are directed to sorting small-diameter DWCNTs, i.e.,DWCNTs having a mean outer wall diameter of less than about 2.0 nm(e.g., less than about 1.7 nm), from large-diameter SWCNTs, e.g., thosehaving a mean diameter of greater than or about 1.4 nm, which has notbeen possible with prior art methods. For ease of comparison withDWCNTs, the diameter of SWCNTs sometimes may be referred herein as theouter wall diameter. It is understood by a person skilled in the artthat a SWCNT consists of a single carbon tubule and therefore can haveonly one diameter.

In addition, while one of the advantages of the present teachingsrelates to simultaneous separation of carbon nanotubes by wall numberand at least one other properties, sorting carbon nanotubes by multipleproperties via more than one separation cycle is within the scope of thepresent teachings.

Accordingly, in some embodiments, the present teachings provide a methodof separating carbon nanotubes by wall number. The present method can beused to sort as-synthesized samples of DWCNTs, which often include amixed population of carbon nanotubes including DWCNTs and SWCNTs, DWCNTsand MWCNTs, or DWCNTS and both SWCNTs and MWCNTs. In addition, the mixedpopulation can include SWCNTs and DWCNTs having overlapping outer walldiameter ranges. For example, the mixed population can include less thanabout 50%, less than about 60%, less than about 70%, less than about75%, less than about 80%, less than about 85%, less than about 90%, orless than about 95% DWCNTs.

The mixed population of carbon nanotubes can be produced by one or moremethods known in the art including chemical vapor deposition such ashigh-pressure carbon monoxide conversion (HiPco), laser ablation, arcdischarge, coalescence, and specific catalytic processes such asCoMoCAT® (SouthWest NanoTechnologies Inc., Norman, OK). In mostembodiments, the mixed population includes pristine or as-synthesizedcarbon nanotubes when applied to the present methods. However, incertain embodiments, carbon nanotubes that have been chemically treatedpost-synthesis (e.g., doped or otherwise irreversibly functionalized)can be used as well.

Current synthetic methods of DWCNTs such as those listed above not onlyproduce significant quantities of unwanted SWCNTs and/or MWCNTs, theyalso produce broad distributions of chiralities and diameters within theDWCNT population and the unwanted SWCNT and/or MWCNT population(s). Forexample, the mixed population can include DWCNTs having outer walldiameter ranges that are between about 0.9 nm and about 3.0 nm. Themixed population also can include SWCNTs having diameter ranges that arebetween about 0.7 nm and about 2.0 nm, for example, between about 0.8 nmand about 1.8 nm. As such, the mixed population can include SWCNTs andDWCNTs having overlapping diameter ranges and outer wall diameterranges, in particular, between about 1.0 nm and about 2.0 nm. Thepresent methods can separate DWCNTs having an outer wall diameter thatis less than about 2.0 nm effectively from SWCNTs having similardiameters. For example, the present methods can separate DWCNTs havingan outer wall diameter that is less than about 1.7 nm from SWCNTs havinga diameter that falls within the same range, i.e., between about 1.1 nmand about 1.8 nm.

In some embodiments, a mixed (or polydisperse) nanotube population canbe contacted with one or more surface active components in a solvent(e.g., water) to provide a dispersion. The one or more surface activecomponents typically associate with the carbon nanotubes non-covalently,providing debundled individual carbon nanotubes “encapsulated” by theone or more surface active components. For example, the one or moresurface active components can associate with the carbon nanotubes by oneor more of ionic interaction, π- π orbital interaction, hydrogenbonding, and Van Der Waals interaction. As used herein, “encapsulate,”“encapsulated,” or “encapsulating” refers to non-covalent associationwith a target such as nanotubes. For example, the one or more surfaceactive components can wrap around the sidewall (circumference) of thecarbon nanotubes, yet not be present at the two ends of the nanotubes.In some embodiments, the surface active components can arrangethemselves around the sidewall of a carbon nanotube as a helicalmonolayer. However, other arrangements, e.g., longitudinal or annulararrangement, are possible.

In various embodiments, nanotubes having different properties exhibitdifferent buoyant densities upon association with (e.g., encapsulationby) the surface active components. The encapsulated nanotube complexesare introduced into a density gradient provided by a fluid medium andcentrifuged. Over the course of the ultracentrifugation, the complexesmove within the density gradient to their respective isopycnic points,that is, where their respective buoyant density matches the density of aparticular layer of the density gradient. Upon sufficient centrifugation(i.e., for a selected period of time and/or at a selected rotationalrate at least partially sufficient to separate the carbon nanotubesalong the medium gradient), the complexes settle into multiple bands ofmaterials according to the desirable characteristic(s) and can beremoved layer by layer from the density gradient to provide separationfractions that primarily contain nanotubes having the desirablecharacteristic(s). The success of a separation can be defined as havingthe complexes settle into distinct bands of materials at differentlocations in the density gradient that are visible to human eye. Forexample, each band of materials can differ in colors or shades ofsimilar colors.

Without limitation to any one theory or mode of operation, separationvia density gradient centrifugation is believed to be driven largely byhow the surface active component(s), for example, surfactant(s),organize around nanotubes of different structure and electronic type.The energetic balance among inter-nanotubes, solvent particles, andsurface active components interactions as well as their packing density,orientation, ionization, and the resulting hydration of these surfaceactive components can all be parameters affecting buoyant density andthe quality of separation and purification. The buoyant density of anencapsulated nanotube in a fluid medium can depend on multiple factors,including the density and electronic character of the nanotube itself,the structure and composition of the surface active component(s)surrounding the nanotube, and the spatial extent of anyelectrostatically bound hydration layers. For DWCNTs and MWCNTs,additional parameters such as intershell interaction and interwallspacing are expected to contribute to unpredictable variations of thebuoyant density of an encapsulated nanotube.

FIGS. 1A-1C illustrate how a particular surface active component (or aparticular system including two or more surface active components) canassociate with and confer different buoyant densities to asmall-diameter single-walled nanotube, a large-diameter single-wallednanotube, and a double-walled nanotube having an outer wall diametersimilar to the diameter of the large-diameter single-walled nanotube.For example, the surface active component can be sensitive to both wallnumber and diameter, such that upon association with the surface activecomponent, the nanotubes can be separated according to their differentbuoyant densities, for example, the nanotubes can have increasingbuoyant density in the order of small-diameter single-walled nanotube,large-diameter single-walled nanotube, and double-walled nanotube. Itshould be understood that a surface active component system comprisesone or more surface active agents.

The one or more surface active components can be selected from a widerange of non-ionic or ionic (cationic, anionic, or zwitterionic)amphiphiles. In some embodiments, the surface active component caninclude an anionic surfactant. For example, a surface active componentcan include one or more sulfates, sulfonates, carboxylates, andcombinations thereof. In certain embodiments, the one or more surfaceactive components can include a compound having a planar polycyclic(e.g., carbocyclic) core. For example, the one or more surface activecomponents can include a compound having a sterane core. In particularembodiments, the one or more surface active components can include oneor more bile salts. Bile salts can be more broadly described as a groupof molecularly rigid and planar amphiphiles with a charged face opposinga hydrophobic face. Examples of bile salts include salts (e.g., sodiumor potassium salts) of conjugated or unconjugated cholates and cholatederivatives including deoxycholates, chenodeoxycholates,taurodeoxycholates, glycochenodeoxycholates, ursodeoxycholates, andglycoursodeoxycholates.

In some embodiments, amphiphiles with anionic head groups and flexiblealkyl tails (interchangeably referred to herein as anionic alkylamphiphiles) can be used. Examples of anionic alkyl amphiphiles includedodecyl sulfates and dodecylbenzene sulfonates such as sodium dodecylsulfate (SDS) and sodium dodecylbenzene sulfonate (SDBS). In certainembodiments, the surface active component can include a cationicsurfactant. For example, such a component can be selected fromamphiphiles with cationic head groups (e.g., quaternary ammonium salts)and flexible or rigid tails. In some embodiments, deoxyribonucleic acid(DNA) such as single-stranded DNA or DNA fragments also can be used asthe surface active component as described in U.S. patent applicationSer. No. 11/368,581, the disclosure of which is incorporated byreference herein in its entirety.

However, to separate effectively nanotubes by wall number and bydiameter, or by wall number and by electronic type, it has been foundthat the surface active component(s) should not interact with thenanotubes in a way that is simultaneously sensitive to both diametersand electronic types. For example, to enable effective separation bywall number and by diameter, the surface active component(s) need to besensitive to diameter but sufficiently insensitive to electronic type,such that, for example, DWCNTs encapsulated by the appropriate surfaceactive component(s) will have significantly higher buoyant densitiesthan SWCNTs having similar diameters regardless of the electronicproperties of the respective shells of the nanotubes. In this regard,planar surface active components have been found useful. As used herein,a planar surface active component refers to a surface active agent thatincludes a geometrically planar portion (e.g., a sterane core) which canhave small substituent(s) thereon. In certain embodiments, the surfaceactive components can consist of sodium cholate (SC).

Similarly, to enable effective separation by wall number and byelectronic type, the surface active component(s) need to be sensitive toelectronic type but sufficiently insensitive to diameter. It has beenfound that two or more surface active components (e.g., a co-surfactantsystem) can be used to effect such separation by selecting a relativeratio of the two or more surface active components that can causenanotubes of a first electronic type (e.g., semiconducting) to have alower buoyant density than nanotubes of a second electronic type (e.g.,metallic), while the nanotubes are simultaneously sorted by wall number.

The two or more surface active components can be of the same type or ofdifferent types. In some embodiments, the two or more surface activecomponents can competitively adsorb to the nanotube surface. Forexample, the at least two surface active components can have differentmolecular geometries and/or different functional groups. Such acompetitive co-surfactant system can be used to achieve optimalseparation between metallic and semiconducting nanotubes. In certainembodiments, the two or more surface active components can include twodifferent bile salts. In some embodiments, the two or more surfaceactive components can include a planar surface active component and alinear surface active component. As used herein, a linear surface activecomponent refers to a surface active agent that includes a linearaliphatic group, for example, a linear aliphatic group with at least sixcarbon atoms. Examples include the various amphiphiles described abovesuch as SDS and SDBS that include a flexible or rigid alkyl tail and acationic or anionic head group.

In some embodiments, the two or more surface active components cancomprise a co-surfactant system including varying amounts of SDS and SC.In certain embodiments, the present method can include using aco-surfactant system that includes a lower ratio of the linear surfaceactive component relative to the planar surface active component toachieve simultaneous separation of nanotubes by wall number and byelectronic type, particularly, with the separation by wall number havinga dominant effect over the separation by electronic type. For example,using a co-surfactant system that includes an SDS:SC ratio of 1:4 (byweight), a mixed population that includes SWCNTs and DWCNTs of bothelectronic types can be expected to separate into four visibly distinctbands of materials (from low to high density) in the order ofsemiconducting SWCNTs (s-SWCNTs), metallic SWCNTs (m-SWCNTs), DWCNTshaving a semiconducting outer wall (s-DWCNTs), and DWCNTs having ametallic outer wall (m-DWCNTs) in a single separation cycle. In otherembodiments, the present method can include using a co-surfactant systemthat includes a higher ratio of the linear surface active componentrelative to the planar surface active component to achieve simultaneousseparation of nanotubes by wall number and by electronic type,particularly, with the separation by electronic type having a dominanteffect over the separation by wall number. For example, using aco-surfactant system that includes an SDS:SC ratio of 3:2 (by weight), amixed population that includes

SWCNTs and DWCNTs can be expected to separate into four visibly distinctbands of materials (from low to high density) in the order of m-SWCNTs,m-DWCNTs, s-SWCNTs, and s-DWCNTs in a single separation cycle.

Generally, density gradient centrifugation uses a fluid medium with apredefined variation in its density as a function of position within acentrifuge tube or compartment (i.e., a density gradient). Fluid mediauseful with the present teachings are limited only by nanotubeaggregation therein to an extent precluding at least partial separation.Accordingly, aqueous and non-aqueous fluids can be used in conjunctionwith any substance soluble or dispersible therein, over a range ofconcentrations, so as to provide the medium a density gradient for usein the separation techniques described herein. Such substances can beionic or non-ionic, non-limiting examples of which include inorganicsalts and alcohols, respectively. Such a medium can include a range ofaqueous iodixanol concentrations and the corresponding gradient ofconcentration densities. As understood by those skilled in the art,aqueous iodixanol is a common, widely used non-ionic density gradientmedium. However, other media can be used in methods of the presentteachings, as would be understood by those skilled in the art.

More generally, any material or compound stable, soluble or dispersiblein a fluid or solvent of choice can be used as a density gradientmedium. A range of densities can be formed by dissolving such a materialor compound in the fluid at different concentrations, and a densitygradient can be formed, for instance, in a centrifuge tube orcompartment. More practically, with regard to choice of medium, thenanotubes, whether or not functionalized (e.g., by means of associationwith one or more surface active components), also should be soluble,stable or dispersible within the fluids/solvent or resulting densitygradient. Likewise, from a practical perspective, the maximum density ofthe gradient medium, as determined by the solubility limit of such amaterial or compound in the solvent or fluid of choice, should be atleast as large as the buoyant density of the particular nanotubes(and/or in composition with one or more surface active components) for aparticular medium.

Accordingly, any aqueous or non-aqueous density gradient medium can beused provided that the nanotubes are stable; that is, do not aggregateto an extent precluding useful separation. Alternatives to iodixanolinclude inorganic salts (such as CsCl, Cs₂SO_(4,) KBr, etc.), polyhydricalcohols (such as sucrose, glycerol, sorbitol, etc.), polysaccharides(such as polysucrose, dextrans, etc.), other iodinated compounds inaddition to iodixanol (such as diatrizoate, nycodenz, etc.), andcolloidal materials (such as Percol 1°). Other parameters which can beconsidered upon choice of a suitable density gradient medium include thediffusion coefficient and the sedimentation coefficient, both of whichcan determine how quickly a gradient redistributes duringcentrifugation. Generally, for more shallow gradients, a largerdiffusion coefficient and a smaller sedimentation coefficient aredesired.

It has been discovered that the point at which the encapsulatednanotubes are introduced into the density gradient in the fluid mediumcan be important to the quality of the separation. In some embodiments,the encapsulated nanotubes are introduced into the density gradient at adensity that is different from the buoyant density of any of theencapsulated nanotubes.

In particular embodiments, a two-iteration DGU process can be used toisolate DWCNTs from SWCNTs of roughly the same outer wall diameter. Forexample, in the first separation cycle, the carbon nanotubes can beloaded at the top of a linear gradient and made to sediment from lowerto higher densities during the ultracentrifugation. By having thenanotubes sediment to higher densities, all the individuallyencapsulated SWCNTs inside the gradient should be unable to reach thedense isopycnic position of the DWCNTs. In contrast, a separation inwhich the nanotubes sediment from higher to lower densities can resultin a poor separation, with a number of slow-moving SWCNTs reaching onlythe DWCNT equilibrium position. After ultracentrifugation, it can beexpected that the SWCNTs and DWCNTs of similar outer wall diameters(e.g., having a mean outer wall diameter of about 1.6 nm) will settleinto two different separation fractions, with the separation fractionenriched with SWCNTs settling above the separation fraction enrichedwith DWCNTs. If the mixed population further includes small-diameterSWCNTs (e.g., SWCNTs having a mean outer wall diameter of less thanabout 1.4 nm), these small-diameter SWCNTs can be expected to settleabove the separation fraction enriched with the larger-diameter SWCNTshaving similar diameters as the DWCNT outer walls. Any carbon nanotubebundles, MWCNTs, and carbonaceous impurities, if present, can beexpected to settle below the separation fraction enriched with DWCNTs.

To achieve further enrichment of DWCNTs, the DWCNT-enriched separationfraction can be subjected to a second iteration of DGU processing. Inthe second separation cycle, the encapsulated DWCNTs can be introducedat the bottom (rather than at the top as in the first separation cycle)of the linear density gradient and made to sediment from high to lowdensities. Because nanotube bundles can be expected to form over time innanotube dispersions, this second iteration helps remove SWCNT bundlesthat may have formed over time in addition to any slow-moving MWCNTsthat did not sediment fast enough in the first iteration. Of course thesecond separation itself can be practiced as a method of the presentteachings, where the starting population of nanotubes is a samplecomprising substantially DWCNTs.

The separation fractions collected according to the procedures describedherein can be sufficiently selective for most current applications ofnanotubes. However, it can be desirable to purify further the separationfractions to improve their selectivity by performing additionaliterations of the present methods. Specifically, a separation fractioncan be provided in a composition with the same surface active componentsystem or a different surface active component system, and thecomposition can be contacted with the same fluid medium or a differentfluid medium, where the fluid medium can have a density gradient that isthe same or different from the fluid medium from which the separationfraction was obtained. In certain embodiments, fluid medium conditionsor parameters can be maintained from one separation to another. In otherembodiments, at least one iterative separation can include a change ofone or more parameters including the identity of the surface activecomponent(s), medium identity, medium density gradient, and/or mediumpH, as well as the duration and the rotational speed of thecentrifugation process, with respect to one or more of the precedingseparations. In certain embodiments, the surfactant(s) encapsulating thenanotubes can be modified or changed between iterations, allowing foreven further refinement of separation. Separation fractions isolatedafter each separation can be washed before further complexation andcentrifugation steps are performed.

The selectivity of the fraction(s) collected can be confirmed by variousanalytical methods including optical absorbance, Raman spectroscopy,transmission emission spectroscopy (TEM), fluorescence spectroscopy, andother methods known in the art.

As described herein, the present teachings provide nanotube populationsthat are substantially monodisperse in terms of wall number as well aspopulations of double-walled nanotubes that are substantiallymonodisperse in terms of their structures and/or properties. In otherwords, such populations generally have narrow distributions of one ormore predetermined structural or functional characteristics. Forexample, in some embodiments, the population can be substantiallymonodisperse in terms of their diameter dimensions (e.g., greater thanabout 75%, including greater than about 90% and greater than about 97%,of the double-walled nanotubes in a population of double-wallednanotubes can have a diameter within less than about 0.5 A of the meandiameter of the population, greater than about 75%, including greaterthan about 90% and greater than about 97%, of the double-walled carbonnanotubes in a population of double-walled nanotubes can have a diameterwithin less than about 0.2 A of the mean diameter of the population,greater than about 75%, including greater than about 90% and greaterthan about 97%, of the double-walled nanotubes in a population ofdouble-walled nanotubes can have a diameter within less than about 0.1 Aof the mean diameter of the population). In some embodiments, thepopulation can be substantially monodisperse in terms of their outerwall electronic type (e.g., greater than about 70%, including greaterthan about 75%, greater than about 80%, greater than about 85%, greaterthan about 90%, greater than about 92%, greater than about 93%, greaterthan about 97% and greater than about 99%, of the double-wallednanotubes in a population of double-walled nanotubes can have asemiconducting outer wall, or greater than about 50%, including greaterthan about 75%, greater than about 90%, greater than about 97%, andgreater than about 99%, of the double-walled nanotubes in a populationof double-walled nanotubes can have a metallic outer wall). In someembodiments, the population can be substantially monodisperse in termsof their outer wall chiralities (e.g., greater than about 30%, includinggreater than about 50%, greater than about 75%, and greater than about90%, of the double-walled nanotubes in a population of double-wallednanotubes can have outer walls having the same chirality (n, m) type).

The nanotube populations of the present teachings can be incorporatedinto various electronic, optical, or optoelectronic devices such asfield-effect transistors, transparent conductors, interconnect devices,sensors, light-emitting diodes, and solar cells, to improve one or moreelectronic and/or optical properties of these devices. The presentnanotube populations can be processed or analyzed ‘as is,’ i.e., withthe individual nanotubes encapsulated by one or more surface activecomponents; alternatively, the surface active components can be removedprior to or during analysis or processing. The one or more surfaceactive components can be removed according to methods known in the art,for example, as disclosed in Meitl et al., Nano Lett., 4: 1643 (2004);and Zhou et al., AppL Phys. Lett., 88: 123109 (2006).

The following examples are provided to illustrate further and tofacilitate the understanding of the present teachings and are not in anyway intended to limit the invention.

EXAMPLE 1 Dispersion of Carbon Nanotubes and Concentration

The starting carbon nanotube material (Batch #: DW331UA) was obtainedfrom Carbon Nanotechnologies Inc. (Houston, Tex.). The sample batch wasindicated by the manufacturer to comprise approximately 70% DWCNTs withouter wall diameters ranging from about 1.5 nm to about 3.0 nm based ontransmission electron microscopy (TEM). Optical absorbance data furthercharacterized that about 22% to about 35% of the DWCNTs in the samplebatch have an outer wall diameter of less than about 1.7 nm.

The carbon nanotube material was added to 110 mL of a 1% w/v sodiumcholate (SC) aqueous solution at a loading of about 2 mg/mL in a steelbeaker. This mixture was cooled in an ice bath, then subjected to hornultrasonication using a 13 mm-diameter tip for 90 minutes at a power of160 W. Following sonication, the dispersion was incorporated directlyinto a step gradient for concentration. The step gradient consisted of adense underlayer of 2 mL of a 1% w/v SC aqueous solution with 60% w/viodixanol topped by approximately 10 mL of the carbon nanotubedispersion. The step gradient was ultracentrifuged in an SW41 Tiswing-bucket rotor (Beckman-Coulter Inc.) at a rotational frequency of41 krpm for 12 hours. Concentrated fractions or bands of carbon nanotubematerials were removed from the centrifuge tube in a two stepfractionation procedure. First, a 1 mL displacement layer consisting ofa 1% w/v SC aqueous solution with 30% w/v iodixanol was slowly infusedinto the gradient to separate poorly dispersed carbon nanotubes from thebuoyant, individually encapsulated carbon nanotubes. After upwarddisplacement, the resulting concentrated band, with a density less than30% w/v iodixanol was removed using a piston gradient fractionator(Biocomp Instruments Inc.).

EXAMPLE 2 Sorting by Wall Number—First Iteration

Carbon nanotubes in the concentrated fraction from Example 1 were sortedby wall number in a gradient containing 1% w/v SC throughout. Thedensity gradient consisted of a 1.5 mL underlayer containing 60% w/viodixanol, followed by a 5 mL linear gradient (SG15, Hoefer Inc.) with adensity varying from 32.5% to 17.5% w/v iodixanol. On top of this lineargradient was added a 1 mL layer containing the concentrated dispersionof carbon nanotubes diluted to a density of 15% w/v iodixanol. Theremaining ˜4.5 mL of the centrifuge tube was filled with 0% w/viodixanol solution. This linear gradient was ultracentrifuged for 12hours at a rotational frequency of 41 krpm in an SW41 Ti rotor, at theend of which isopycnically separated SWCNTs and DWCNTs were produced.

FIG. 2A is a photograph of a centrifuge tube 100 containing a dispersionof a polydisperse carbon nanotube sample taken after one separationcycle according to the present methods, which resulted in the dispersionseparating into four colored bands located at different buoyantdensities. Band 102 corresponds to small-diameter SWCNTs; band 104corresponds to large-diameter SWCNTs; band 108 corresponds to DWNTs; andthe thick black band 110 includes very dense MWNTs, carbonaceousimpurities, and bundled nanotubes. The transparent band 106 issubstantially free of carbon nanotube materials.

To confirm these qualitative assignments, these bands of separatedmaterials were extracted from the centrifuge tube using a pistongradient fractionator (Biocomp Instruments, Inc.) and characterized byoptical absorbance (FIG. 2B). The topmost band 102 exhibits multiplediscrete peaks in the visible and near infrared that can be assigned tooptical transitions associated with SWCNTs having a diameter of about0.7 nm to about 1.2 nm (curve 112). For the carbon nanotubes located inthe band below (band 114), the optical absorbance (curve 114 a) containstwo broad peaks ranging from about 640 nm to about 860 nm and from about900 nm to about 1300 nm that can be attributed to metallic andsemiconducting SWCNTs, respectively, with average diameters of about 1.6nm. For the DWCNT band (band 108), the optical absorbance (curve 118 a)is similar to that of the large diameter SWCNTs indicating the DWCNTouter walls are of comparable diameter to the SWCNTs. In addition, atransition at about 1190 nm, discussed in more detail below, isindicative of absorbance from the inner walls of the DWCNTs. The opticalabsorbance of the dense, broad black band 110 exhibits furtherred-shifting of the semiconducting and metallic transitions as well asincreased background absorbance (data not shown) which is consistentwith nanotubes of larger diameters, as well as increased bundling andcarbonaceous impurity content. Curves 116 and 120 correspond to theabsorbance spectra of the transparent band 106 and the startingmaterial, respectively.

Of these materials, a 2 mm thick band (band 104 in FIG. 2A) with anaverage density of 17.8% iodixanol (1.095 g/mL) was selected for asecond iteration of sorting for its high large-diameter SWCNT content.Furthermore, a 2.5 mm thick band (band 108 in FIG. 1a ) with an averagedensity of 21.5% iodixanol (1.115 g/mL) was selected for a seconditeration of sorting as a result of its large DWCNT content.

EXAMPLE 3 Sorting by Wall Number—Second Iteration

The SWCNT- and DWCNT-enriched fractions were isolated and introducedinto separate gradients consisting of the following layers, each with 1%w/v SC content. First, a dense, 1.5 mL underlayer of 60% w/v iodixanolwas added to the bottom of the centrifuge tube, followed by a 1 mL layerof the enriched fraction diluted to a density of 33.5% w/v iodixanol. A5 mL linear gradient with density running from 31% to 16% w/v iodixanolwas added above the carbon nanotube layer and was topped by a ˜4.5 mLlayer with a density of 1 g/mL. This gradient was then ultracentrifugedin an SW41 Ti for 12 hours at 41 krpm. Following centrifugation, bandsof isolated carbon nanotubes were recovered from the centrifuge tubeusing a piston gradient fractionator.

Absorbance spectra of the highly enriched SWCNT fraction (DGU-SWCNTs,curve 114 b) and the highly enriched DWCNT fraction (DGU-DWCNTs, curve118 b) show significant improvement in sorting quality after twoiterations (FIG. 2B). Compared to curves 114 a and 118 a, both materialsexhibit decreased peak widths and lower background absorbance levels,which can be attributed to decreased numbers of bundled carbon nanotubesand smaller amounts of carbonaceous impurities.

EXAMPLE 4 Characterization by Transmission Electron Microscopy

DGU-DWCNTs, initially dispersed in water with SC and iodixanol, wereprecipitated by diluting the nanotube dispersion with water to bring theSC concentration to less than 0.1% w/v, and subsequently diluted withisopropanol to completely withdraw the SC from the carbon nanotubesidewalls. The precipitates were filtered through anodized aluminumoxide membranes (Whatman Anodisc), and rinsed with copious amounts ofwater to remove the remaining SC and iodixanol. The resulting carbonnanotube films were immersed in acetone and freed from the membranesusing bath sonication. The acetone in turn was removed by heating at 90°C. for two hours leaving solid, surfactant-free sorted carbon nanotubematerial.

The DGU-DWCNTs were redispersed in 3 ml of a 1% w/v sodium dodecylsulfate (SDS) solution in deuterated water (D₂O) using a hornultrasonicator (Fisher Scientific Model 500 Sonic Dismembrator). Theultrasonicator was equipped with a 3 mm diameter tip and operated at 15%amplitude for 90 minutes while the sample was cooled in an ice bath.Poorly dispersed carbon nanotube bundles were removed byultracentrifugation for 14 minutes at 38 krpm in a Beckman CoulterTLA100.3 rotor. A 5 μL droplet from the top 2.5 mL layer of thedispersion was deposited on TEM grids coated with an ultrathin (<3 nm)carbon film (Prod. #01824, Ted Pella, Inc.). After ˜30 seconds, the gridwas dried using filter paper and rinsed in deionized water. The grid wasthen dried again using filter paper.

TEM images taken on JEOL JEM-2100F Fast TEM confirmed that the DGU-DWNTspredominantly consisted of double-walled species.

EXAMPLE 5 Characterization and Diameter Determination Using RamanSpectroscopy

Previous studies of DWCNTs have revealed substantial differences in theRaman spectra of DWCNTs and SWCNTs following treatment with concentratedsulfuric acid and have been used to assess DWCNT content (see Kim etal., Chem. Phys. Lett., 420: 377 (2006); Barros et al., Phys. Rev. B,76: 045425 (2007); and Filho et al., Nano Lett., 7: 2383 (2007)).

To confirm that the increased buoyant densities and absorbancecharacteristics of DGU-DWCNTs did not arise from SWCNTs with bimodaldiameter distributions, Raman spectra were obtained on thin film samplesof DGU-SWCNTs and DGU-DWCNTs. Specifically, DGU-SWCNTs and DGU-DWCNTswere processed into thin films of—60% transmittance on glass and quartzsubstrates (see Wu et al., Science, 305: 1273 (2004)). For comparison,thin films of HiPco-SWCNTs (Carbon Nanotechnologies Inc.) andarc-discharge-grown SWCNTs (AD-SWCNTs, Carbon Solutions Inc.) havingsimilar diameters to the inner walls and the outer walls of DGU-DWCNTsalso were prepared on the same transparent substrates. Based on theoptical absorbance of the DGU-DWCNTs, Raman spectra were measured at twodifferent excitation wavelengths: 514.5 nm to probe DWCNTS havingsemiconducting outer walls and metallic inner walls, and 750 nm to probeDWCNTS having metallic outer walls and semiconducting inner walls (FIG.3). The radial breathing mode (RBM) and G band spectra obtained fromthese samples (FIG. 3A and FIG. 3C) are consistent with the assignmentsderived from optical absorbance (FIG. 2B).

Because SWCNT diameters can be related to the RBM frequencies with theequation (ORBM=A/dt+B (see Bachilo et al., Science, 298: 2361-2366(2002)), the values of A and B were first determined using the Ramanspectra of thin films of as-produced HiPco-SWCNTs having a knownchirality distribution. The RBM frequencies and diameters of theHiPco-SWCNTs were well described by a fit with A=218.2 and B =19.6.

To evaluate the mean diameters of the DGU-DWCNTs, the average RBMfrequencies of the peaks associated with the inner wall and the outerwall of DWCNTs were calculated. These RBM frequencies were thenconverted to carbon nanotube diameters and corrected to account fordifferences in the laser power. The calculations revealed that theDGU-DWCNTs have mean inner wall diameters of ˜0.86 nm and mean outerwall diameters of ˜1.61 nm.

To ensure that signals arising from small-diameter carbon nanotubes weredue to the inner wall of DWCNTs and not small-diameter SWCNT impurities,optical measurements were performed before and after the DGU-DWCNTs weresubjected to chemical treatments selected to strongly affect the opticalproperties of the outer wall of the DWCNTs. Because the inner wall ofDWCNTs should be isolated from adsorbed species by the protective outerwall, the optical characteristics of the inner nanotubes would belargely unaffected by the chemical treatment, unlike any SWCNTimpurities.

Thin film samples of DGU-SWCNTs and DGU-DWCNTs were chemically treatedby coating them with concentrated sulfuric acid (95-98%) for 10 minutes,after which any excess acid was removed using a jet of nitrogen gas, andthe films were left to dry over several days.

FIG. 3A shows the Raman spectra of the four nanomaterials(HiPco-SWCNTs—122, AD-SWCNTs—124, DGU-SWCNTs—126, and DGU-DWCNTs—128)measured as pristine films (solid curves, a) and films treated withsulfuric acid (dashed curves, b) at 514.5 nm excitation. FIG. 3B showsspectra from the carbon nanotube tangential modes (HiPco-SWCNTs—132,AD-SWCNTs—134, DGU-SWCNTs—136, and DGU-DWCNTs—138) before (solid curves,a) and after (dashed curves, b) acid treatment at 514.5 nm excitation.FIG. 3C shows the Raman spectra of the four nanomaterials(HiPco-SWCNTs—142, AD-SWCNTs—144, DGU-SWCNTs—146, and DGU-DWCNTs—148)measured as pristine films (solid curves, a) and films treated withsulfuric acid (dashed curves, b) at 750 nm excitation. FIG. 3D showsspectra from the carbon nanotube (HiPco-SWCNTs—152, AD-SWCNTs—154,DGU-SWCNTs—156, and DGU-DWCNTs—158) tangential modes before (solidcurves, a) and after (dashed curves, b) acid treatment at 750 nmexcitation.

As described above, the Raman spectra 128 a, 148 a of DGU-DWCNTs exhibitRBMs corresponding to inner walls (162, 166) having an average diameterof —0.86 nm and outer walls (160, 164) having an average diameter of˜1.61 nm. For DGU-SWCNTs 126 a, 146 a, the RBMs attributable to smalldiameter carbon nanotubes (c.f. HiPco-SWCNTs 122 a, 142 a) arecompletely absent at 514.5 nm and weak in intensity at 750 nmexcitation. Moreover, the RBMs associated with large diameter nanotubes(c.f. AD-SWCNTs 124 a, 144 a) indicate the DGU-SWCNTs have an averagediameter of —1.60 nm, similar to the outer wall diameter of DGU-DWCNTs(128 a, 148 a).

The G-bands of the pristine SWCNT samples have peak shapes that can beadequately described by two Lorentzians corresponding to the G′ and G⁻bands (FIG. 3B and FIG. 3D). Conversely, the DGU-DWCNT sample exhibits aG-band (FIG. 3B and FIG. 3D) with a finer structure with two pairs of G′and G⁻ bands attributable to both the inner and outer tubes (see Kim etal., Chem. Phys. Lett., 420: 377 (2006)).

Following acid treatment, all carbon nanotube films showed decreasedRaman signal intensity and marked changes in their RBMs and G-band.Referring back to FIG. 3, pristine carbon nanotube films (solid curves)display significantly higher intensity than films treated with sulfuricacid (dashed curves). For both the control SWCNT samples (i.e.,HiPco-SWCNTs and AD-SWCNTs) and DGU-SWCNTs, RBMs were almost completelysuppressed by the sulfuric acid treatment. However, as shown in FIG. 3,for DGU-DWCNTs, protection protected by the outer wall (as indicated bythe shaded regions 160 and 164) preserves much of the RBM intensity ofthe inner wall (as indicated by the shaded regions 162 and 166)following acid doping. Meanwhile, RBMs associated with the outer wallswere significantly reduced. In addition, the degree of inner-wall RBMattenuation was similar to that observed for the G-band of DGU-DWCNTs,indicating that much of the decrease in RBM intensity was due to changesin film morphology and thickness following acid treatment, not fromlarge amounts of impurity SWCNTs.

For the tangential modes, the G′ components for the SWCNTs and the DWCNTouter walls were upshifted by at least 5 cm“⁻¹ following acid treatment.In contrast, the G′ component corresponding to the inner walls of theDWCNTs was essentially fixed in frequency with a small upshift of ˜1cm”⁻¹ as a result of the chemical resistance afforded by the outer wall.

Differences in the optical properties of pristine and thionyl chloridedoped SWCNTs and DWCNTs were studied to provide further evidence ofsorting by wall number. Thin films of HiPco-SWCNTs, AD-SWCNTs,DGU-SWCNTs, and DGU-DWCNTs were immersed in the acceptor-type dopantthionyl chloride (see U. Dettlaff-Weglikowska et al., J. Am. Chem. Soc.127, 5125 (2005)) for 12 hours followed by drying in air for another 12hours.

FIGS. 4A-4D show optical absorbance spectra of thin films ofHiPco-SWCNTs (162), AD-SWCNTs (164), DGU-SWCNTs, (166), and DGU-DWCNTs(168) before (solid curves, a) and after (dashed curves, b) exposure tothionyl chloride. The absorbencies of the four pristine spectra werenormalized to the it-plasmon at about 280 nm with the spectra of thedoped films scaled by the same factor. The first-order, second-order,and third-order semiconducting optical transitions are shaded andlabeled S11, S22, and S33; and the first-order and second-order metallicoptical transitions are shaded and labeled M11 and M22.

Before doping, all four sets of films exhibited strong absorbance as aresult of metallic and semiconducting chiralities as labeled in FIGS.4A-4D. For the three SWCNT samples and the outer wall of the DGU-DWCNTs,thionyl chloride treatment completely suppressed the first-ordersemiconducting transitions (S11) as a result of large shifts in theFermi level induced by the dopant molecules. Other peaks associated withthe second-order semiconducting transitions (S22) and first-ordermetallic transitions (M11) also were attenuated and broadened but couldstill be identified following treatment. In contrast, the DGU-DWCNT filmmaintains several sharp and intense absorption peaks in the S22, S33,and M11 regions as indicated by arrows in FIGS. 4A-4D before and afterchemical treatment. Furthermore, the peaks corresponding to innersemiconducting carbon nanotubes in the 1,050 nm to 1,250 nm wavelengthregion displayed considerably smaller line widths than those ofsemiconducting HiPco-SWCNTs of the same diameter. Peak broadeningtypically occurs for SWCNTs as a result of increased nanotube-nanotubeinteractions when SWCNTs form bundles in thin films. The absence of peakbroadening observed for the transitions in DGU-DWCNTs is yet furtherevidence that the inner walls of the DWCNTs are protected from theexternal environment by the outer carbon nanotube shell.

EXAMPLE 6 Length Distribution of Sorted Carbon Nanotubes

Following optical characterization, the length distribution ofDGU-SWCNTs and DGU-DWCNTs were quantified using atomic force microscopy(AFM). AFM samples were prepared as follows.

Preparation of AFM samples: Surfactant-encapsulated carbon nanotubeswere deposited on SiO ₂ capped Si wafers via a(3-aminopropyl)triethoxysilane (APS; Sigma-Aldrich) self-assembledmonolayer. The monolayer was formed by immersing the Si wafers in 2.5 mMAPS aqueous solution for at least 30 minutes. Following immersion, thewafers were dried under nitrogen gas, rinsed in deionized water, anddried again. To improve the yield of the deposition, the carbon nanotubedispersions were diluted into a 2% w/v SDS aqueous solution(Sigma-Aldrich). A 10 μL drop of the diluted dispersion was then placedon the silanized substrate and allowed to dry over 10 minutes. Theremaining solution was blown off with nitrogen gas, and the wafer wasrinsed in deionized water to remove adsorbed surfactant molecules. Afterdrying with nitrogen, the wafers covered with carbon nanotubes atsub-monolayer coverage were heated at 250° C. in air for one hour toremove any remaining surfactants and iodixanol.

AFM images were obtained using a Thermo Microscopes AutoprobeCP-Research AFM operating in tapping mode. Conical AFM probes with aCr—Au backside coating were used for all measurements (MikroMasch,NSC36/Cr—Au BS). Images 5 μm×5 μm in size were analyzed for determiningthe DGU-SWCNT and DGU-DWCNT length distributions and typically contained10 to 30 carbon nanotubes each. Intersecting nanotubes whose paths couldnot be clearly identified and those that were clearly part of bundleswere not included in the analysis.

The lengths of 356 individual DGU-SWCNTs and 392 individual DGU-DWCNTswere measured over multiple AFM images and compiled into the histogramshown in FIG. 5. The DGU-SWCNTs (open bars) were found to have anaverage length of about 626 nm, while the DGU-DWCNTs (shaded bars) weredetermined to be about 44% longer on average, with a mean length ofabout 904 nm. Both length distributions were found to follow log-normaldistributions as indicated by the solid and dashed curves in FIG. 5. Thedifference in carbon nanotube length as a function of wall number can beattributed to improved mechanical properties of DWCNTs compared toSWCNTs. In particular, the sonication used to disperse carbon nanotubesinto surfactant solution is known to decrease nanotube length as aresult of tube cutting. However, DWCNTs, with the mechanicalreinforcement of their inner wall, are expected to be more resistant tosonication-induced cutting compared to SWCNTs. Because both theDGU-SWCNTs and DGU-DWCNTs were exposed to identical sonicationconditions, it follows that the DWCNT material should exhibit longeraverage lengths than the SWCNTs, assuming both classes of material hadthe same initial length distribution.

The observed resistance to tube cutting could be particularly beneficialin thin film applications of carbon nanotubes. The performance of thinfilm devices consisting of networks of carbon nanotubes previously hasbeen hindered by two interrelated factors: nanotube polydispersity andnanotube length. Most applications of carbon nanotube thin films, suchas flexible field effect transistors and transparent conductors, canbenefit greatly from the use of carbon nanotubes that are monodispersein both electronic type and diameter (see Arnold et al., NatureNanotech., 1:60 (2006); and Green et al., Nano Lett., 8: 1417 (2008)).However, to allow processing, carbon nanotube bundles need to beseparated into individual carbon nanotubes on a large scale.Unfortunately, ultrasonication, the most common separation technique,reduces carbon nanotube length and as a result, increases the number ofnanotube-nanotube junctions required for charge transport across thenetwork, thereby impairing nanotube network performance. In view of theabove, DWCNTs could prove to be an ideal class of carbon nanotubes forthin film device applications because they can maintain relatively longaverage lengths even after aggressive sonochemistry.

EXAMPLE 7 Transparent Conductive Coatings Including Sorted CarbonNanotubes

To test the thin film advantages of DGU-DWCNTs, DGU-DWCNTs wereincorporated into a series of transparent conductive coatings and theirperformance was compared to that of DGU-SWCNTs films and films preparedfrom unsorted

DWCNT materials. Specifically, the unsorted DWNT film samples wereprepared from the same dispersion of sonicated carbon nanotubes used toproduce the DGU-SWCNT and DGU-DWCNT materials (Example 1). A 1.5 mLvolume of this starting dispersion was centrifuged for 30 minutes at16,000 relative centrifugal force (Eppendorf Microcentrifuge 5424). Thetop 1.0 mL of solution, free of large bundles and poorly solubilisedmaterial, was decanted carefully and incorporated into control films ofunsorted DWCNTs using vacuum filtration and transferred to glasssubstrates (see Wu et al., Science, 305: 1273 (2004)).

The sheet resistance and optical transmittance of the films weremeasured using a four-point probe and a spectrophotometer (Cary 500,Varian Inc.), respectively. For quantitative assessment of the behaviorof each transparent conductive material, the experimental data was fitto the following equation:

$\begin{matrix}{T = \left( {1 + {\frac{1}{2\;{Rs}}\sqrt{\frac{\mu_{0}}{ɛ_{0}}}\frac{\sigma_{op}}{\sigma_{d\; c}}}} \right)^{- 2}} & (1)\end{matrix}$where R_(s) is the sheet resistance, T is the wavelength dependenttransmittance, (T_(op) is the optical conductivity which varies as afunction of wavelength, σ_(dc) is the direct current conductivity, andμ₀ and ε_(o) are the permeability and permittivity of free space,respectively. Equation 1 has been used previously to describe thebehavior of carbon nanotube transparent conductors (see Hu et al., NanoLett., 4: 2513 (2004); and Zhou et al., Appl. Phys. Lett., 88: 123109(2006)) and is particularly valuable in assessing the performance ofDGU-processed material, because the sole fitting parameterσ_(op)/σ_(dc), can be used to concisely quantify the performanceimprovement offered by different carbon nanotube materials (see Green etal., Nano Lett., 8: 1417 (2008)).

For pristine DGU-DWCNTs at a wavelength of about 550 nm, σ_(op)/σ_(dc)is 0.12 compared to 0.29 for DGU-SWCNTs and 0.58 for unsorted materials(FIG. 6A). This difference implies that transparent conductorscontaining DGU-DWCNTs are approximately 2.4 times and 4.8 times moreconductive than those containing DGU-SWCNTs and unsorted nanotubes,respectively. As a result, a pristine DGU-SWCNT transparent conductorwould have a sheet resistance of ˜352 Ω/□ at 75% transmittance while aDGU-DWCNT film at the same transmittance would provide a sheetresistance of ˜146 Ω/□.

To further enhance the electrical conductivity of the films, the carbonnanotube thin films were doped with thionyl chloride using the sameprocedure employed when studying the effects of doping on nanotubeoptical absorbance. Doping increased the thin film conductivity of theDGU-DWCNTs, DGU-SWCNTs and unsorted nanotubes by factors of 2.2, 3.8 and2.0, respectively, at 550 nm (FIG. 6B). The differences in the effectsof doping between the sorted materials could be due in part to highermetallic carbon nanotube content in the DGU-DWCNTs compared to theDGU-SWCNTs as indicated by differences in the relative intensities offirst-order metallic and semiconducting transitions in the DGU-SWCNTsand DGU-DWCNTs (FIGS. 4A-4D). In addition, the presence of inner wallsin the DWCNTs could mitigate some of the effects of the adsorbeddopants. The lower conductivity of unsorted nanotubes compared toDGU-DWCNTs and DGU-SWCNTs can be explained by the presence ofcarbonaceous impurities in unsorted films that are typically removedduring sorting. These impurities not only reduce the conductivity ofpristine unsorted films, but also do not respond as strongly to chemicaldoping. Despite the larger conductivity increase demonstrated by theDGU-SWCNTs after thionyl chloride exposure, doped DGU-DWCNT films stillexhibited ˜42% higher conductivity than doped DGU-SWCNT networks.Furthermore, doped films generated from more weakly sonicated, longerDGU-DWCNTs produced sheet resistances as low as 40 Ω/□ at 70%transmittance at a wavelength of 550 nm. The exemplary properties of theDGU-DWCNT films make them promising candidates for high-performancetransparent conductor applications.

EXAMPLE 8 Sorting of Carbon Nanotubes by Both Wall Number and Outer WallElectronic Type

Sorting by both wall number and (outer wall) electronic type wereconducted in gradients with density profiles identical to thosedescribed in Examples 2 and 3 but with different surfactant loadings.The density profiles consisted of a 1.5 mL, 60% iodixanol underlayer,followed by a 1 mL carbon nanotube layer with a density of 35% w/viodixanol. On top of this layer was a 5 mL linear gradient withdensities ranging from 32.5% to 17.5% w/v iodixanol that was topped by a˜4.5 mL overlayer with 0% w/v iodixanol.

FIG. 7A and FIG. 7C show photographs of centrifuge tubes 200 and 300each containing a dispersion of a polydisperse carbon nanotube sample(including a mixture of large-diameter SWCNTs and DWCNTs) after oneseparation cycle according to the present methods. The samples shown inFIG. 7A and FIG. 7C were sorted using surface active components designedto optimize separation of DWCNTs having a semiconducting outer wall(s-DWCNTs) and DWCNTs having a metallic outer wall (m-DWCNTs),respectively. For semiconductor enrichment, the overall surfactantloading was set to 1% w/v with a 1:4 SDS/SC ratio (by weight); hence,the gradient contained 0.2% w/v SDS and 0.8% w/v SC. For metallicenrichment, the overall surfactant loading was also 1% w/v with a 3:2SDS/SC ratio. The two density gradients were ultracentrifuged in a SW41Ti rotor for 12 hours at a rotational frequency of 41 krpm. Followingultracentrifugation, the carbon nanotubes enriched by electronic typewere removed using a piston gradient fractionator.

Referring to FIG. 7A, two pairs of colored bands of sorted materialappeared in the centrifuge tube 200. The upper bands were produced fromSWCNTs sorted by electronic type (s-SWCNT band 202 in red, m-SWCNT band204 in green) while the lower pair of bands corresponded to DWCNTssorted by electronic type which possessed higher buoyant densities as aresult of the density of the inner DWCNT wall (s-DWCNT band 206 in red,m-DWCNT band 208 in green).

Referring to FIG. 7C, again two pairs of colored bands of sortedmaterial appeared in the centrifuge tube 300. However, the upper pair ofbands are both green in color this time (m-SWCNTs 302, m-DWCNTs 304)suggesting metallic nanotubes, while the lower pair of bands are bothred in color, suggesting semiconducting nanotubes (s-SWCNTs 306,s-DWCNTs 308).

Optical absorbance spectra confirmed the band assignment (FIGS. 6b and6d ). Enrichment by electronic type is evidenced by changes in therelative amplitude of transitions associated with metallic andsemiconducting chiralities in each of the bands. Enrichment in metalliccarbon nanotubes (214, 218, 312, 314) is indicated by strong absorbancein the wavelength ranges (M11, M22) associated with metallic carbonnanotubes and weak absorbance in the ranges (S22, S33) associated withsemiconducting carbon nanotubes, while enrichment in semiconductingspecies (212, 216, 316, 318) is evidenced by the converse. DWCNTS (solidcurves) are marked by characteristic optical absorbance peaks associatedwith their inner walls (labeled with arrows) that are absent in theabsorbance of SWCNTs (dashed curves). The absorbance of the startingmaterial is represented by curves 220 and 320.

EXAMPLE 9 Comparison with State-of-the-Art High-Purity, As-SynthesizedDouble-Walled Carbon Nanotubes

The literature has reported as-synthesized DWCNTs that are nominallyabout 95% pure. See Endo et al., Nature, vol. 433, 476 (2005), and Kimet al., Chem. Vap. Deposition, vol. 12, 327-330 (2006).

To compare the purity of these state-of-the-art materials with those ofthe sorted DWCNTs of the present teachings (“DGU-DWCNTs”), Raman spectraof DGU-DWCNTs were collected at nearly the same excitation energies andcompared to the data reported in Barros et al., Phys. Rev. B, 76: 045425(2007) (“Barros data”). The Barros data include Raman spectra of undopedDWCNTS (solid curves) and DWCNTs doped with H₂SO₄ (dashed curves), andare shown in FIG. 8A. Data of DGU-DWCNTs are shown in FIG. 8B. As can beseen from these spectra, the Barros DWCNTs and DGU-DWCNTs have verysimilar diameters (about 1.6 nm outer diameter and about 0.9 nm innerdiameter) as indicated by similar frequencies of RBM peaks.

The DGU-DWCNTs only have two small peaks that can be identified asSWCNTs (as a result of their extreme diameters; indicated by arrows inFIG. 8B). In contrast, many peaks that can be associated with SWCNTs areapparent in the Barros data (see FIG. 8A). For instance, the shadedregion covering frequencies ranging from about 200 cm⁻¹ to about 225cm⁻¹ contains strong RBM peaks at multiple excitation energies. Thesepeaks are associated with nanotubes of about 1 nm to about 1.2 nm.Because the interwall spacing of DWCNTs is about 0.7 nm, if these 1-1.2nm diameter nanotubes are the inner walls of DWCNTs, their outer wallsmust be about 1.7 nm to about 1.9 nm in diameter. However, no RBM peakscorresponding to nanotubes having this outer wall diameter can beobserved in the Barros data (marked by the shaded region coveringfrequencies ranging from about 125 cm⁻¹ to about 145 cm⁻¹).Consequently, these Raman data suggest that DGU-DWCNTs according to thepresent teachings are of higher purity than the state-of-the-artas-synthesized DWCNTs reported in the literature.

EXAMPLE 10 Further Enrichment of Double-Walled Carbon Nanotubes byElectronic Type

Carbon nanotubes (Batch #: DW411UA) obtained from CarbonNanotechnologies, Inc. (Houston, Tex.) were dispersed into a 1% w/v SCaqueous solution as described in Example 1. The dispersion wasconcentrated and coarsely sorted by wall number in a singlecentrifugation step. This processing was accomplished by forming a 7 mLlinear density gradient containing 1% w/v SC that varied from 25% w/viodixanol to 40% w/v iodixanol and adding approximately 31 mL of thecarbon nanotube solution on top. The resulting density gradient wasultracentrifuged in an SW28 rotor (Beckman-Coulter Inc.) for 22 hours ata rotational frequency of 28 krpm. The sorted carbon nanotubes were thenremoved from the centrifuge tube in a two step fractionation procedure.First, a 4 mL displacement layer consisting of 1% w/v SC aqueoussolution with 40% w/v iodixanol was slowly infused into the gradient toseparate poorly dispersed carbon nanotubes from the buoyant,individually encapsulated materials. After upward displacement, thesorted carbon nanotube fractions with densities less than 40% w/viodixanol were removed using a piston gradient fractionator (BiocompInstruments Inc.). Following characterization using optical absorbance,the fractions with the highest DWCNT content were selected forelectronic type sorting.

Selective Separation of Double-Walled Carbon Nanotubes Having a MetallicOuter Wall

Fractions highly enriched in DWCNTs having a metallic outer wall(“highly enriched m-DWCNTs”) were produced in a two-iteration sortingprocess with density gradient parameters summarized in Table 1. In thefirst iteration, the DWCNT enriched material was injected at the bottomof the linear density gradient and the nanotubes moved upward in thedensity gradient during ultracentrifugation. This step removed densecarbon nanotube bundles and multi-walled carbon nanotubes, and resultedin pairs of metallic carbon nanotube and semiconducting carbon nanotubebands similar to those shown in FIG. 7C. Fractions enriched in m-DWCNTsfrom the first iteration were then placed at the top of the lineardensity gradient for the second iteration. As a result, buoyant, slowsedimenting SWCNTs were removed from the material during this separationleaving highly enriched m-DWCNT material in the denser regions of thegradient.

TABLE 1 m-DWCNT DGU Parameters First Iteration Second IterationSurfactant 1% w/v 3:2 SDS/SC throughout 1% w/v 3:2 SDS/SC throughoutOverlayer 4.5 mL, 0% w/v iodixanol 8 mL, 0% w/v iodixanol Position ofBottom of linear gradient Top of linear gradient Nanotube Layer NanotubeLayer 1 mL, 37.5% w/v iodixanol; 10 mL, 3% w/v iodixanol; m- DWCNTenriched material DWCNT enriched material from first iteration LinearDensity 5 mL, 20% to 35% w/v iodixanol 15 mL, 25% to 40% w/v iodixanolGradient Underlayer 1.5 mL, 60% w/v iodixanol 5 mL, 60% iodixanolUltracentrifugation SW41 Ti, 12 hours at 41 krpm and SW28, 22 hours at28 krpm and 22° C. Parameters 22° C.Selective Separation of Double-Walled Carbon Nanotubes Having aSemiconducting Outer Wall

Fractions highly enriched in DWCNTs having a semiconducting outer wall(“highly riched s-DWCNTs”) were produced in a three-iteration sortingprocess with density gradient parameters summarized in Table 2. In thefirst iteration, the DWCNT enriched material was injected at the bottomof the linear density gradient and the nanotubes moved upward in thedensity gradient during ultracentrifugation. This step removed densecarbon nanotube bundles and multi-walled carbon nanotubes, and resultedin a pair of SWCNT and DWCNT bands similar to those shown in FIG. 7A.Fractions enriched in s-DWCNTs from the first iteration were then placedat the top of the linear density gradient for the second iteration. As aresult, most buoyant, slow sedimenting SWCNTs were removed from thematerial during this separation leaving enriched s-DWCNT material in thedenser regions of the gradient. Optical absorbance of these s-DWCNTsrevealed the presence of >1.7 nm diameter m-SWCNTs. A third iteration in1% w/v 3:2 was utilized to remove these impurity species, which bandedin a lower density region of the gradient following ultracentrifugation.

TABLE 2 s-DWCNT DGU Parameters First Iteration Second Iteration ThirdIteration Surfactant 1% w/v 1:4 SDS/SC 1% w/v 1:4 SDS/SC, 1% w/v 3:2SDS/SC throughout except nanotube layer throughout Overlayer 4.5 mL, 0%w/v 8 mL, 0% w/v 2 mL, 0% w/v iodixanol iodixanol iodixanol Position ofBottom of linear Top of linear gradient Top of linear gradient NanotubeLayer gradient Nanotube Layer 1 mL, 37.5% w/v 10 mL, 3% w/v 3.5 mL, 3%w/v iodixanol; iodixanol; s-DWCNT iodixanol; s-DWCNT DWCNT enrichedenriched material from enriched material from material first iteration;1% w/v second iteration SC with small amount of SDS Linear Density 5 mL,20% to 35% w/v 15 mL, 25% to 40% w/v 5 mL, 25% to 40% w/v Gradientiodixanol iodixanol iodixanol Underlayer 1.5 mL, 60% w/v 5 mL, 60%iodixanol 1.5 mL, 60% iodixanol iodixanol Ultracentrifugation SW41 Ti,12 hours at 41 SW28, 22 hours at 28 SW41 Ti, 12 hours at 41 Parameterskrpm and 22° C. krpm and 22° C. krpm and 22° C.Characterization of Highly Enriched s-DWCNTs and m-DWCNTs

Highly enriched s-DWCNTs and m-DWCNTs were characterized by opticalabsorbance and Raman spectroscopy to confirm enrichment by wall numberand electronic type. FIG. 9 shows the optical absorbance from thesematerials in aqueous solution. The spectrum acquired from s-DWCNTsexhibits strong absorption peaks in the S22 and S33 regions associatedwith outer wall semiconducting transitions, while the absorption in theM11 region arising from metallic outer wall species is stronglysuppressed. These features are consistent with outer wall semiconductorenrichment. The opposite behavior in the S22, S33, and M11 regions canbe seen in the m-DWCNT material, which is consistent with outer wallmetal enrichment. Weak peaks marked by arrows in FIG. 9 can beattributed to the DWCNT inner walls.

The optical absorbance of thin films of highly enriched s-DWCNTs andm-DWCNTs were measured to more conclusively identify optical transitionsfrom the inner wall of the DWCNTs. Pristine thin films of the highlyenriched s-DWCNTs (FIG. 10A, solid curve) and highly enriched m-DWCNTs(FIG. 10B, solid curve) exhibited strong absorbance peaks in the outerwall semiconductor (S11, S22, and S33) and metal (M11) transitionranges, respectively. Upon doping with thionyl chloride (dashed curvesin FIG. 10A and FIG. 10B), the absorption peaks arising from the DWCNTouter walls were suppressed, leaving the inner wall transitions largelyunaffected due to the protection afforded by the outer wall. These innerwall transitions are labeled with arrows and confirm that thesematerials contain predominantly double-walled species.

For further evidence of isolation by outer wall electronic type, Ramanspectra were obtained from s-DWCNT and m-DWCNT films using a laserexcitation wavelength of 514.5 nm (FIG. 11). This wavelength wasselected because it is in resonance with the semiconducting DWCNT outerwalls and the metallic DWCNT inner walls. For both materials, RBM peaksin the 240 cm⁻¹ to 360 cm⁻¹ range corresponding to nanotube diameters of0.64 nm to 0.99 nm can be observed, a diameter range expected for DWCNTinner walls. In contrast, the strong RBM peak in the 150 cm′ to 190 cm⁻¹range corresponding to outer wall diameters of 1.28 nm to 1.67 nmobserved in the s-DWCNT material is suppressed by ˜85% in the m-DWCNTs.Because predominantly s-DWCNTs are excited at 514.5 nm, the weakness ofthis particular RBM peak in the m-DWCNTs confirms that the materialcontains only low levels of s-DWCNTs.

Calculation of Purity Levels of Highly Enriched s-DWCNTs and m-DWCNTs

The level of enrichment by electronic type of the m-DWCNTs and s-DWCNTswas calculated following an established method (see Green et al., NanoLett., 8: 1417 (2008)). In this analysis, optical absorbance spectrawere used to calculate the areas in energy space of the first ordermetallic (M11) and first order semiconducting (S11) absorbance peaks ofthe m-DWCNTs and s-DWCNTs, as well as a control sample of unsortedAD-SWCNTs with known one-third metallic carbon nanotube content. Theabsorbance areas of the AD-SWCNT sample were then used to determine theextinction coefficient of the metallic carbon nanotubes, which was foundto be a factor of 1.5 less than that of semiconducting carbon nanotubes.With this relative extinction factor, the percent metallic purities ofthe sorted DWCNTs were calculated using the following equation:% Metallic Purity=1.5×(M11 Area)/[1.5×(M11 Area)+(S11 Area)]

The absorbance peak areas and calculated metallic purity levels arepresented in Table 3. Intermediate levels of percent metallic purity canbe obtained by combining different amounts of m-DWCNTs and s-DWCNTs.

TABLE 3 m-DWCNT and s-DWCNT Electronic Type Purity Levels Area ofAbsorbance Peak % Metallic Sample M11 S11 Purity AD-SWCNTs 2.44 7.3133.3% m-DWCNTs 41.6 2.62 96.0% s-DWCNTs 0.532 19.1 4.0%

EXAMPLE 11 Field-Effect Transistors Produced from Thin Films of HighlyEnriched s-DWCNTs and Highly Enriched m-DWCNTs

Thin film field-effect transistors were fabricated with the highlyenriched s-DWCNT materials (“s-DWCNT devices”) and the highly enrichedm-DWCNT materials (“m-DWCNT devices”) as the active layer in thedevices, respectively. To prepare these devices, gold/palladiumelectrodes were first defined on degenerately doped silicon waferscapped by a 100 nm thick dry thermal oxide. Percolating thin filmnetworks of s-DWCNTs and m-DWCNTs produced by vacuum filtration weretransferred onto the wafers and annealed in air for 20 minutes at 225°C. The devices were tested with a probe station (M-150, CascadeMicrotech Inc.) inside a light-tight enclosure using two source meterunits (KE2400, Keithley Inc.). Gate voltages were applied through thesilicon substrate and gate leakage currents were monitored to ensurethat they did not contribute significantly to the measured source-draincurrent. The devices have channel lengths and widths of 4 μm and 250 nm,respectively.

Transfer curves for the s-DWCNT devices (solid curves) and the m-DWCNTdevices (dashed curves) are shown in FIG. 12A. While both types ofdevices were modulated in response to the gate voltage and had similaron currents, the s-DWCNT network exhibited an on/off ratio ˜100 largerthan that of the m-DWCNT network. The higher switching ratio of thes-DWCNT devices was expected as a result of its high semiconductorcontent. The switching ratio of a film of metallic single-walled carbonnanotubes was reported to be ˜2 (see Arnold et al., Nature Nanotech., 1:60 (2006)). The higher on/off ratio observed in the m-DWCNT devicescould be due to current modulation through the semiconducting innerwalls of the m-DWCNTs.

FIG. 12B presents the variations in on/off ratios and on currents forthe s-DWCNT devices (open symbols) and the m-DWCNT devices (closedsymbols) at 2 μm (squares) and 4 [tm (triangles) channel lengths. Asignificant increase in on/off ratios (10²) for the s-DWCNT devices wasobserved at various on currents and for both channel lengths. Treatingthe s-DWCNT network as a uniform semiconducting film (see Arnold et al.,Nature Nanotech., 1: 60 (2006)), it is possible to extract a lower boundfor the mobility of these devices from the linear region of the transfercurve. This analysis results in effective mobilities of ˜7.6 cm²/V-s and˜4.2 cm²/V-s for the s-DWCNT devices of 2 μm and 4 μm channel lengths,respectively.

The present teachings encompass embodiments in other specific formswithout departing from the spirit or essential characteristics thereof.The foregoing embodiments are therefore to be considered in all respectsillustrative rather than limiting on the present teachings describedherein. Scope of the present invention is thus indicated by the appendedclaims rather than by the foregoing description, and all changes thatcome within the meaning and range of equivalency of the claims areintended to be embraced therein.

Some references, which may include patents, patent applications andvarious publications, are cited and discussed in the description of thisinvention. The citation and/or discussion of such references is providedmerely to clarify the description of the present invention and is not anadmission that any such reference is “prior art” to the inventiondescribed herein. All references cited and discussed in thisspecification are incorporated herein by reference in their entiretiesand to the same extent as if each reference was individuallyincorporated by reference.

What is claimed is:
 1. A method of separating carbon nanotubes,comprising: centrifuging complexes of encapsulated nanotubes in contactwith a first fluid medium comprising a first density gradient, so thatthe encapsulated nanotubes settle into multiple bands at differentlocations in the first density gradient according to one or moreproperties of the encapsulated nanotubes and are removable layer bylayer from the first density gradient to provide separation fractions,each separation fraction being enriched with the encapsulated nanotubesaccording to the one or more properties of the encapsulated nanotubes,wherein the complexes comprise a carbon nanotube population comprising acarbon nanotube population comprising double-walled carbon nanotubeshaving a semiconducting outer wall (s-DWCNTs) and double-walled carbonnanotubes having a metallic outer wall (m-DWCNTs) individuallyencapsulated by two or more surface active components comprising aplanar surface active component and a linear surface active component,and wherein the one or more properties comprise wall number and/or outerwall electronic type; and separating the centrifuged complexes alongsaid first density gradient to obtain said separation fractions, whereinsaid separation fractions comprise a first separation fraction enrichedwith the s-DWCNTs having a carbon nanotube subpopulation comprising apercentage of the s-DWCNTs higher than that of the s-DWCNTs in thecarbon nanotube population, and a second separation fraction enrichedwith the m-DWCNTs having a carbon nanotube subpopulation comprising apercentage of the m-DWCNTs higher than that of the m-DWCNTs in thecarbon nanotube population.
 2. The method of claim 1, wherein the carbonnanotube population further comprises semiconducting single-walledcarbon nanotubes (s-SWCNTs) and metallic single-walled carbon nanotubes(m-SWCNTs), and wherein after the centrifuging step, said separationfractions comprise at least four separation fractions, the at least fourseparation fractions comprising the first separation fraction, thesecond separation fraction, a third separation fraction enriched withthe s-SWCNTs having a carbon nanotube subpopulation comprising apercentage of the s-SWCNTs higher than that of the s-SWCNTs in thecarbon nanotube population, and a fourth separation fraction enrichedwith the m-SWCNTs having a carbon nanotube subpopulation comprising apercentage of the m-SWCNTs higher than that of the m-SWCNTs in thecarbon nanotube population.
 3. The method of claim 2, wherein therelative ratio of the two or more surface active components is selectedto cause metallic carbon nanotubes to have a lower buoyant density thansemiconducting carbon nanotubes regardless of wall number.
 4. The methodof claim 2, wherein the relative ratio of the two or more surface activecomponents is selected to cause semiconducting carbon nanotubes to havea lower buoyant density than metallic carbon nanotubes of the same wallnumber.
 5. The method of claim 2, wherein the relative ratio of the twoor more surface active components is selected to cause metallic carbonnanotubes to have a lower buoyant density than semiconducting carbonnanotubes of the same wall number.
 6. The method of claim 2, wherein therelative ratio of the two or more surface active components is selectedto cause semiconducting carbon nanotubes to have a lower buoyant densitythan metallic carbon nanotubes regardless of wall number.